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Universal covering spaces and fundamental groups in algebraic geometry as schemes
algebraic geometry fundamental groups
2015/7/14
In topology, the notions of the fundamental group
and the universal cover are closely intertwined. By importing
usual notions from topology into the algebraic and arithmetic setting, we construct a ...
ALGEBRAIC STRUCTURES ON THE TOPOLOGY OF MODULI SPACES OF CURVES AND MAPS
MODULI SPACES CURVES AND MAPS
2015/7/14
We discuss selected topics on the topology of moduli spaces
of curves and maps, emphasizing their relationwith GromovWitten theory and integrable systems
MURPHY’S LAW IN ALGEBRAIC GEOMETRY: BADLY-BEHAVED DEFORMATION SPACES
LAW IN ALGEBRAIC GEOMETRY DEFORMATION SPACES
2015/7/14
We consider the question: “How bad can the deformation space of an object
be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as possible...
ALGEBRAIC ALGORITHMS FOR SAMPLING FROM CONDITIONAL DISTRIBUTIONS
Structure markov chain algorithm the discrete sampling statistical index family conditions spectral analysis data
2015/7/14
We construct Markov chain algorithms for sampling from discrete
exponential families conditional on a sufticient statistic. Examples include
contingency tables, logistic regression, and spectral a...
Derived Representation Theory and the Algebraic K-theory of Fields
Algebraic K-theory of Fields Derived Representation Theory
2015/7/7
Quillen’s higher algebraic K-theory for fields F has been the object of intense
study since their introduction in 1972 [26]. The main direction of research has
been the construction of “descen...
Structured Stable Homotopy Theory and the Descent Problem for the Algebraic K-theory of Fields
Structured Stable Homotopy Theory Algebraic K-theory
2015/7/7
his is a relative result which asserts that the K-theory spectra of any two
algebraically closed fields of a given characteristic are equivalent to each other
after completion at a prime not e...
Let k be a eld, and let G be an algebraic group over k, by which we mean a connected smooth k-group
scheme (not necessarily ane). Recall that such a G is automatically separated, nite type, and ge...
This paper is largely concerned with constructing quotients by etale equivalence relations.
We are inspired by questions in classical rigid geometry, but to give satisfactory answers in that categor...
We prove the niteness of class numbers and Tate-Shafarevich sets for all ane group
schemes of nite type over global function elds, as well as the niteness of Tamagawa
numbers and Godement's com...
Semidefinite Programming Relaxations and Algebraic Optimization in Control
Control Algebraic Optimization
2015/6/19
We present an overview of the essential elements of semidefinite programming as a computational tool for the analysis of systems and control problems. We make particular emphasis on general duality pr...
Hesitating progress–the slow development toward algebraic symbolization in abbacus- and related manuscripts, c.1300 to c.1550
algebraic symbolization abacus related manuscripts
2015/3/26
Hesitating progress–the slow development toward algebraic symbolization in abbacus- and related manuscripts, c.1300 to c.1550.
Polyhedral Divisors, Dedekind Domains and Algebraic Function Fields
Polyhedral Divisors Dedekind Domains Algebraic Function Fields
2012/7/11
In this paper, we show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We describe also a class of multigraded a...
The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces
Toric Varieties Algebraic K-Theory Weighted Projective Spaces K-regularity
2012/7/11
We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\K$-theory (denoted $\KH$-theory) entirely in terms of the torus pieces of open sets forming an open cover of ...
Three lectures on Algebraic Microlocal Analysis
Three lectures Algebraic Microlocal Analysis Algebraic Geometry
2012/6/27
These three lectures present some fundamental and classical aspects of microlocal analysis. Starting with the Sato's microlocalization functor and the microsupport of sheaves, we then construct a micr...
Rigidification of algebras over essentially algebraic theories
homotopy limit theory homotopy model rigidification
2012/6/18
Badzioch and Bergner proved a rigidification theorem saying that each homotopy simplicial algebra is weakly equivalent to a simplicial algebra. The question is whether this result can be extended from...